Una pene makes no sense. Also it would technically be penecillo, with a c. However, we do use polla which is akin to dick/cock and is feminine. We also say coño which means vagina and that is masculine
in portuguese we have something similar. "pênis", "pinto" and "pau" are masculine, but "piroca" is feminine.
why so many words for the same thing? good question! i have no idea!
btw if you want to know what each one means:
pênis: penis
pinto: closest translation in this meaning would be "cock" but the other, more common, meaning is "chick" as in a baby chicken
pau: literally means stick and can be used to refer to a penis. (thankfully there's also "graveto" which means stick but people don't think about a penis when they hear it)
piroca: i don't know if there is any meaning for this word other than dick or penis, and im pretty sure it's some variation of "pinto", made to sound goofier (and it seems it's feminine just because it ends with an A)